Sequences and Series

Front

What is a sequence?

Back

A set of numbers a1, a2, ..., an, ... such that to each positive integer n, there corresponds a number an of the set, denoted by {an}.

Front

What is an example of a sequence where an = 1/n?

Back

The sequence is 1, 1/2, 1/3, ..., 1/n, ...

Front

What is a constant sequence?

Back

A sequence where all terms are the same, e.g., an = k.

Front

What is a finite sequence?

Back

A sequence that has a finite number of terms.

Front

What is an infinite sequence?

Back

A sequence that does not have a finite number of terms.

Front

What is a bounded sequence?

Back

A sequence {sn} is said to be bounded if there exist numbers m, M such that m < an < M for all n in N.

Front

What is a monotonic sequence?

Back

A sequence that is either monotonically increasing or monotonically decreasing.

Front

What is the limit of a sequence?

Back

The limit l of a sequence {sn} is said to exist if for every ε > 0, there exists m in Z+ such that |sn - l| < ε for all n ≥ m.

Front

What is a convergent sequence?

Back

A sequence {sn} is said to be convergent if it has a finite limit.

Front

What is a divergent sequence?

Back

A sequence {sn} is divergent if its limit is infinite.